# Whitehead groups may be not free, even assuming CH, I

@article{Shelah1977WhiteheadGM, title={Whitehead groups may be not free, even assuming CH, I}, author={Saharon Shelah}, journal={Israel Journal of Mathematics}, year={1977}, volume={28}, pages={193-204} }

AbstractWe prove the consistency with ZFC+G.C.H. of an assertion, which implies several consequences of
$$MA + 2^{\aleph _0 } > \aleph _1 $$
, which
$$\diamondsuit \aleph _1 $$
implies their negation.

#### 75 Citations

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$$
\diamondsuit _{\omega _1 }
$$
called ♣ (club), is… Expand

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Abstract We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two ℵ 1 -separable abelian groups of cardinality ℵ 1 which are… Expand

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Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ1 are exactly the strongly ℵ1-free groups. Some consequences of the assumption that… Expand

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We show that it is consistent with ordinary set theory ZFC and the generalized continuum hypothesis that there exist two א1-separable abelian groups of cardinality א1 which are filtration-equivalent… Expand

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- 1981

For abelian groups, ifV=L, Ext(G, Z) cannot have cardinality ℵ0. We show that G.C.H. does not imply this. See Hiller and Shelah [2], Hiller, Huber and Shelah [3], Nunke [5] and Shelah [6, 7, 8] for… Expand

The monadic theory of (ω2, <) may be complicated

- Mathematics, Computer Science
- Arch. Math. Log.
- 1992

SummaryAssume ZFC is consistent then for everyB⫅ω there is a generic extension of the ground world whereB is recursive in the monadic theory ofω2.

A model with Suslin trees but no minimal uncountable linear orders other than $\omega_1$ and $-\omega_1$

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We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner.… Expand

The uniformization property for ℵ2

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- 1980

AbstractWe present S. Shelah’s result thatS12={δ<ω2: cf(δ)=ω1} may have the uniformization property (cf., §1, or [3] for a definition) for “well-chosen sequences”, 〈ηδ:δ∈S12^ηδ an… Expand

Iterated souslin forcing, the principles ⋄(E) and a generalisation of the axiom SAD

- Mathematics
- 1978

AbstractThe axiom SAD was introduced in our paper with Avraham and Shelah [1]. It is a Martin’s Axiom type of principle, having some of the consequences of MA plus
$$2^{\aleph _0 } > \aleph _1 $$
,… Expand

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